The problem of ensuring compatibility of mixed partial derivative vectors of surface patches joining G2-continuously around a common nodepoint is essential in modelling G2-continuous nsided surfaces. Although the compatibility constraints can be removed by using C2 Gregory patches, these patches have singularities at their comer points. This paper presents conditions for ensuring the compatibility of the mixed partial derivative vectors of surface patches joining GZ-continuously around a common nodepoint. After investigating the solvability of these compatibility conditions, a new solution method exploiting G3-continuity of surface patches at a common nodepoint is given. Example surfaces based on this solution method are also provided.